When you look at Termesphere paintings you get a sense
of geometric order. Why would a painting of Notre Dame in Paris on a sphere
give you the feeling of order? What are these orders?

WHAT
IS A TERMESPHERE

What you are seeing when you look at a Termesphere
painting is an inside-out view of a total physical world around you on the
outside surface of the hanging and rotating sphere. If you were on the inside
of the sphere this painted image around you would seem normal but I make you
read it from the outside. >From any point you look at the spherical
painting, the image reads correctly. Termespheres capture the up, down and all
around visual world from one revolving point in space. Most of the time these
spheres are painted on the outside so it takes a six point perspective system
to keep all of this environment around you organized.

I
have been painting spherical paintings since 1968-9 when I received my Masters
Degree in Art at the University of Wyoming. I continued to do my thesis on the
Termesphere at Otis Art Institutes in Los Angeles for the next two years. I
received my MFA in design there.

HOW
THIS CONCEPT WAS FOUND FROM INSIDE A BOX

The
idea of capturing total visual space around you on the sphere or six point
perspective came to me in a very odd way. I had been studying and teaching
perspective for a number of years. It advanced up to four point perspective but
I wasn't satisfied. The main development happened when I focused my attention
on perspective while working on my Masters Degree in art at the University of
Wyoming. After having come up with some drawings and designs on paper which
showed different ways to think of six point perspective, I attempted to put it
to use. I decided I would build a small cubical object I could crawl into. This
cube would have an exaggerated perspective built into it like my drawings
showed. My thought was if you could pull the corners of the cube in toward the
center of the cube it would give you the illusion it was a much larger box. I
started to imagine what this cube would look like. A fellow student told me it
would look like a cube painted on a sphere. The cube would become the sphere if
you pulled its corner in far enough. I went back to my studio and tried to
construct a cube on a kid's ball. I realized in order to draw the cube
accurately on the sphere all the lines of the cube must aim to the center of
the adjacent faces of the cube. All the lines became greater circles. If each
of the lines of this cube were drawn all the way to the point you would
construct a rhombic dodecahedron (twelve diamonds). The points in the center of
the cube would create the vertices of the octahedron.

When
I looked at this cubical structure on the sphere as a drawing, I had the
feeling I could be inside this cube. What if I thought of this cube as a room
and I were inside of it? If this cube were thought of as a drawing of a room,
the points in the center of each face would be thought of as vanishing points
in perspective. The rule in Renaissance one and two point perspective says that
all parallel lines converge at the same vanishing point. These parallel line on
my cube were projecting in two directions to the center of the adjacent faces.
Counting the points of projection it came to six, the same number as the faces
of the cube. The lines which came from the four corner of the center square
projected out by me. This thinking was inside out but the bottom face of the
cube was the floor, the top face of the cube was the ceiling and the four other
faces were the four walls. If you put tables and chairs on the floor, hang
light fixtures from the ceiling tile and cut windows and doors into the walls,
you have a room rather than just a cube and it is the inside of a room on the
outside of the spherecube.

THE
GEOMETRY

What
are some of the unique geometries going on in this room on a sphere? If the
furniture and other objects in the room are parallel to the room, every line
which creates this room or furniture for the room would bisects the sphere if
it were continued. Every cubical object created for this room projects to all
six equal distant vanishing points. All parallel lines go to two vanishing
points. If a railroad track vanishes to a point in front of you, it will also vanish
to one behind you. All you have to do is turn around and look.

INSIDE
OR OUTSIDE THE SPHERECUBE

The
thing that helps to make this all more sensible is to think of yourself inside
the sphere looking out. If your eye is in the direct center of the sphere and
you are looking at this cube room painted on the sphere it would look very
normal. If you were inside and in the center of a real room and your head were
inside a transparent sphere and you copied what you saw outside the sphere onto
the inside surface of the sphere, it would look exactly the same as the cube
painted on the outside of the sphere.

IN
THE SPHERE

Another
experiment is to imagine having a transparent sphere on you head and place six
equal distant large dots on it like the vertices of the octahedron. With the
sphere on your head, arrange the dots so that one dot is above your head and
another dot is below your head. The other four dots are parallel to the horizon
around you. Now, walk into a cubical building. With one eye in the center of
the sphere rotate the sphere until one of the points on the sphere overlaps
with one of the vanishing points of the building. Keep the four dots on the
sphere parallel to the ground. With your eye in the center of the transparent
sphere, notice where the other five vanishing points of the building are
located. All of the building's vanishing points will line up with the dots you
put on the sphere. This is the way it would work. This will work this way no
matter where you locate yourself within the building. Can you see why people
see mathematics when looking at the Termesphere?

The
following Termespheres illustrate my point. Some are real places, some are
imaginary environments and some are geometric worlds. Think of yourself inside
the sphere.

HAGIA SOPHIA is a 24" diameter sphere. This painting allows you to
float about 40 feet off the floor to view the inside of this wonderful
Christian and Moslem structure. This building is based upon the cube, a cube
with a dome on the top.

INSPIRATIONS FOR ESCHER is a 16" diameter sphere which hangs and
rotates from a ceiling motor. This shows M.C. Eschers in his favorite small
town of Ravillo, Italy. Around him are found ideas which later become his great
works of art.

CHAPEL OF THE ANGELS is
a 16" diameter spherical painting. This chapel is found in Ravillo, Italy.
It is an example of six point perspective on the sphere.

ST PETERS is a 16" diameter spherical painting. This sphere shows
the combination of curves and cubical straight lines which compose this great
building all wrap onto the surface of the sphere. Any direction you look at
this painting, it reads correctly.

FISSION
OF THE CHECK is a 24" diameter spherical painting. Cubes grow from a
checker board pattern. Another set of cubes also grow from the diagonal of that
first check system. This sphere could be said to hold ten points of
perspective.

CONCAVE BUBBLES is a
24" diameter sphere. There a 100 reflective ball that float through this
room each reflecting the room from the location they are within the room. If
they are floating high in the room they reflect mostly the floor. If they are
floating low in the room they reflect mostly the ceiling. Each bubble is
slightly different.

SAINTE
CHAPELL IN PARIS is a 24" diameter sphere. You are above the floor some
thirty feet so you can look straight across at the stain glass windows. This
shows how detailed a basic cubical room can get.